Australian Mining Company's Bet on Rare-Earth Elements Is in Danger of Going Sour

SYDNEY—Lynas Corp. has spent a decade and hundreds of millions of dollars trying to break China's stranglehold on the supply of rare-earth elements, but now the Australian mining company's shareholders worry that its big bet might have gone sour.

When prices of rare earths used in products such as iPads surged three years ago, Lynas's value shot up to roughly two billion Australian dollars (US$1.88 billion) on expectations that its...